Question

A pollen grain has a maximum electric charge it can carry before the electric field it generates exceeds the dielectric limit for air of 3 × 10 6 N / C . 3×106 N/C. Estimate the magnitude of the maximum voltage V max Vmax at the surface of a pollen grain that is carrying its maximum electric charge, assuming V = 0 V=0 at infinity.

Answer 1

Answer:

18 V

Explanation:

Let

r = Radius of pollen grain = $6\times 10^{-6}\ m$ (general value)

E = Electric field = $3\times 10^6\ N/C$

Electric field is given by

$E=\dfrac{kq}{r^2}$

Voltage is given by

$V=\dfrac{kq}{r}$

$\dfrac{V}{E}=r\\\Rightarrow V=Er\\\Rightarrow V=3\times 10^6\times 6\times 10^{-6}\\\Rightarrow V=18\ V$

The maximum voltage is 18 V